Short Term Price Fluctuations (Continued)
I have constructed tables of conditional probabilities. They may be easier to understand. They show what happened to prices when P/E10 fell within specified ranges during the years of 1921 through 1980.
New Tables
I extracted monthly (nominal) prices from January 1921 through December 1980 and P/E10 from Professor Robert Shiller’s database. I determined the lowest price within the following 1, 2 and 5 years (12, 24 and 60 months) and divided it by the original price. Similarly, I determined the highest price within the following 1, 2 and 5 years. Again, I expressed it as a ratio relative to the original price.
Then, I sorted the data into deciles. Each decile contains 72 of the 720 months of data. I sorted each set of data according to outcomes (i.e., the minimum and maximum price ratios within the following 1, 2 or 5 years). I counted the number months within each decile for which P/E10 was below 10, between 10 and 15, between 15 and 20, between 20 and 25 and above 25.
Each sorting process was totally independent of the others.
Finally, I converted the number of months of each cell to the percentage of months within its range of P/E10 values.
Price Dips
The following tables show the worst price dips. They show the worst monthly prices of the S&P500 during the following 1, 2 and 5 years throughout 1921-1980 as a percentage of months within each P/E10 range.
PERCENTAGES FOR THE WORST MONTHS: lowest prices in the following year
Pmin(1yr)/P..<10..10to15..15to20..20to25..>25
0.33 to 0.78 4 6 15 17 38
0.78 to 0.85 1 7 14 17 46
0.85 to 0.90 9 11 9 8 15
0.90 to 0.93 9 14 8 6 0
0.93 to 0.96 12 10 10 8 0
0.96 to 0.98 9 11 9 13 0
0.98 to 1.00 16 8 9 11 0
1.00 to 1.02 12 11 7 12 0
1.02 to 1.04 11 13 7 8 0
1.04 to 1.29 16 9 12 2 0
PERCENTAGES FOR THE WORST MONTHS: lowest prices in the following two years Pmin(2yr)/P..<10..10to15..15to20..20to25..>25
0.22 to 0.67 3 1 18 16 92
0.67 to 0.79 1 10 13 15 8
0.79 to 0.86 4 10 12 16 0
0.86 to 0.90 9 12 9 10 0
0.90 to 0.93 9 12 9 9 0
0.93 to 0.96 15 10 9 8 0
0.96 to 0.99 14 10 8 9 0
0.99 to 1.01 14 11 8 8 0
1.01 to 1.03 12 14 5 6 0
1.03 to 1.24 17 10 9 4 0
PERCENTAGES FOR THE WORST MONTHS: lowest prices in the following five years Pmin(5yr)/P..<10..10to15..15to20..20to25..>25
0.15 to 0.58 1 1 15 23 100
0.58 to 0.70 1 6 28 0 0
0.71 to 0.79 1 12 10 18 0
0.79 to 0.85 4 10 6 28 0
0.86 to 0.90 9 13 7 12 0
0.90 to 0.94 11 13 8 5 0
0.94 to 0.97 16 11 8 4 0
0.97 to 1.00 18 11 6 4 0
1.00 to 1.02 17 13 4 6 0
1.02 to 1.24 21 11 7 1 0
Lessons about Price Dips
Higher P/E10 levels portend bad news. This becomes readily apparent at the extreme where P/E10 is above 25.
Lower P/E10 levels suggest better outcomes. This is most apparent at the opposite extreme where P/E10 is below 10.
It takes more than a single year to reach worst case conditions.
P/E10 levels below 15 protect against a permanent price decrease of 50%.
Price Increases
The following tables show the highest price increases. They show the highest monthly prices of the S&P500 during the following 1, 2 and 5 years throughout 1921-1980 as a percentage of months within each P/E10 range.
PERCENTAGES FOR THE BEST MONTHS: highest prices in the following year
Pmax(1yr)/P..<10..10to15..15to20..20to25..>25
0.81 to 1.00 4 8 15 13 23
1.00 to 1.03 5 10 12 14 0
1.03 to 1.06 4 10 13 13 8
1.06 to 1.09 7 10 8 20 0
1.09 to 1.12 6 9 11 15 8
1.12 to 1.16 12 11 9 10 0
1.16 to 1.20 16 9 9 7 8
1.20 to 1.26 17 8 10 1 38
1.26 to 1.33 13 13 9 2 0
1.34 to 2.24 18 12 4 5 15
PERCENTAGES FOR THE BEST MONTHS: highest prices in the following two years Pmax(2yr)/P..<10..10to15..15to20..20to25..>25
0.85 to 1.03 1 6 18 14 23
1.03 to 1.07 4 8 11 22 8
1.08 to 1.11 3 9 11 21 8
1.11 to 1.16 7 10 12 13 0
1.16 to 1.22 6 10 11 13 15
1.22 to 1.28 9 9 10 11 31
1.28 to 1.34 16 9 13 0 0
1.34 to 1.43 22 11 5 0 15
1.43 to 1.56 22 13 3 2 0
1.57 to 2.37 10 15 6 5 0
PERCENTAGES FOR THE BEST MONTHS: highest prices in the following five years Pmax(5yr)/P..<10..10to15..15to20..20to25..>25
0.86 to 1.11 0 2 24 14 38
1.11 to 1.21 0 6 12 30 8
1.21 to 1.32 0 7 12 25 38
1.32 to 1.40 0 9 15 16 15
1.40 to 1.54 9 8 15 10 0
1.55 to 1.63 10 13 10 3 0
1.63 to 1.77 17 13 7 2 0
1.77 to 1.98 20 14 4 0 0
1.98 to 2.20 14 18 2 0 0
2.20 to 3.80 31 11 0 0 0
Lessons about Price Increases
P/E10 levels above 20 seldom lead to a 50% price increase over the following 5 years. A 50% price increase at Year 5 corresponds to an 8.4% annualized price-only return (nominal).
All of the conditions with P/E10 levels starting below 10 ended up with a price increase above 40% at Year 5.
P/E10 levels above 20 behaved similarly to those above 25. P/E10 levels below 15 behaved similarly to those below 10.
By Year 5, price-only returns sort themselves with higher returns corresponding to lower levels of P/E10. There is a certain amount of abruptness in this sorting. Almost all P/E10 levels above 15 are similar. Almost all P/E10 levels below 15 are similar.
This pattern becomes more and more evident over time. It is not very clear (except for P/E10 below 10) at Year 1. It begins to emerge by Year 2. It is obvious in Year 5.
Conclusions
Today’s P/E10 is close to 27. The upside is limited. The downside could last several years.
These data provide only a starting point. They are descriptive of what has happened. They do not come with a guarantee.
P/E10 ratios of 15 to 20 define a region of short-term uncertainty that often leads to an unfavorable outcome by Year 5. Expect good news to follow when P/E10 is below 15.
Have fun.
John Walter Russell
November 8, 2006